On the reversal bias of the Minimax social choice correspondence

TL;DR

This paper investigates the reversal bias in social choice correspondences, establishing conditions under which the Minimax method is immune, and compares it with Borda and Copeland methods using graph theory.

Contribution

It introduces three qualifications of reversal bias and characterizes when Minimax is immune, using a novel graph-theoretic approach and arithmetical conditions.

Findings

Minimax is immune to reversal bias under specific arithmetical conditions.

The paper provides a new characterization of the Minimax correspondence.

It discusses reversal bias issues for Borda and Copeland correspondences.

Abstract

We introduce three different qualifications of the reversal bias in the framework of social choice correspondences. For each of them, we prove that the Minimax social choice correspondence is immune to it if and only if the number of voters and the number of alternatives satisfy suitable arithmetical conditions. We prove those facts thanks to a new characterization of the Minimax social choice correspondence and using a graph theory approach. We discuss the same issue for the Borda and Copeland social choice correspondences.